DOI:10.1140/epjb/e2013-40258-1
Regular Article
PHYSICAL
JOURNAL
B
Membership in social networks and the application
in information filtering
Wei Zeng1,2, An Zeng2,a, Ming-Sheng Shang1,3,b, and Yi-Cheng Zhang1,2,3
1 Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China,
Chengdu 611731, P.R. China
2 Department of Physics, University of Fribourg, Chemin du Mus´ee 3, 1700 Fribourg, Switzerland 3 Institute of Information Economy, Hangzhou Normal University, Hangzhou 310036, P.R. China
Received 27 March 2013 / Received in final form 27 June 2013
Published online 9 September 2013 – c EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2013
Abstract. During the past few years, users’ membership in the online system (i.e. the social groups that
online users joined) were widely investigated. Most of these works focus on the detection, formulation and growth of online communities. In this paper, we study users’ membership in a coupled system which contains user-group and user-object bipartite networks. By linking users’ membership information and their object selection, we find that the users who have collected only a few objects are more likely to be “influenced” by the membership when choosing objects. Moreover, we observe that some users may join many online communities though they collected few objects. Based on these findings, we design a social diffusion recommendation algorithm which can effectively solve the user cold-start problem. Finally, we propose a personalized combination of our method and the hybrid method in [T. Zhou, Z. Kuscsik, J.G. Liu, M. Medo, J.R. Wakeling, Y.C. Zhang, Proc. Natl. Acad. Sci. 107, 4511 (2010)], which leads to a further improvement in the overall recommendation performance.
1 Introduction
Clustering is one of the most important features in so-cial systems. Network representation of these systems al-lows us to identify communities which are distinguished by the density of links higher in communities than among them [1]. In the past, many methods have been pro-posed to detect these kinds of structure-based communi-ties, such as modularity maximizing method [2], signaling method [3] and spectral clustering method [4]. Recently, a significant community structure was detected in the on-line marketing network [5]. Communities have concrete applications [1]. For instance, one can set up efficient rec-ommendation systems by identifying clusters of customers with similar interests in the customers-products bipartite network (e.g., www.amazon.com) [6]. Moreover, commu-nity information and link prediction can benefit from each other [7–9].
Recently, another kind of community in online com-mercial systems also received much attention. In some on-line social networking sites, such as MySpace and Live-Journal, users with the same interest can join one group and share information with each other. Due to the rapid development of these sites, this kind of online groups is becoming increasingly prominent and widely investigated.
a e-mail: an.zeng@unifr.ch
b e-mail: shang.mingsheng@gmail.com
These explicit user-defined groups are quite different from the structure-based communities. The online groups are created by online individuals while the structure commu-nity are detected by algorithms. Yang and Leskovec [10] defined these kinds of groups as ground-truth communi-ties. In reference [11], the formation of online groups in two large social networks is studied. They show that the tendency of an individual to join a group is influenced not just by the number of friends he/she has within the group, but also crucially affected by how those friends are con-nected to each other. Besides, reference [12] studies the life and death of online groups. They find that a group attracts new members through the friendship ties of its current members to outsiders.
To the best of our knowledge, few work investigates the relation between the online groups and users’ choices of objects so far. In reality, it always happens that a user makes his/her decision on choosing an object by referring to other user’s comments. In this case, the comments from the group mates can be very valuable to the user. Besides, one can find like-minded users in the online group and directly adopts the items selected by these users. There-fore, the membership (i.e. the social groups that online users joined) will inevitably influence individuals’ choices of objects. However, this process is not easy to be directly studied since there is no record about through which way users select objects in real cases. In this paper, we adopt
Table 1. The statistics of datasets.
Dataset #user #objects #groups #user-objects pairs #user-group paris
Last.fm 27 500 22 443 20 341 1 503 938 309 633
Douban 25 039 25 182 2 635 2 107 251 121 810
a mathematical framework called the Aspect Model which allows us to calculate the potential influence of the social grouping on users’ selection of objects [13]. Specifically, we compute the probability that a user can find his/her interested objects from the group mates’ selected objects. If the probability is high, we consider the potential influ-ence of groups on this user’s choice of object to be large. The analysis is based on a coupled system which includes both the user-group and user-object bipartite networks. Our results show that small degree users are more likely to be influenced by the membership than large degree users. Moreover, we observe from empirical data that some users who have collected a few objects may join many groups. The results suggest that the data of social groups can be very valuable in information filtering [14].
Recommendation, as a typical information filtering technique, has been intensively studied in recent years by physicists [15–23]. One of the biggest challenges in recommendation is the user cold-start problem. In on-line systems, the new/inactive users have only expressed few ratings or collected few objects, which makes recom-mendation algorithms fail to accurately predict the ob-jects these users are interested in. In real online systems, web sites are competing for users. In order to attract more users, web sites should provide new/inactive users with more accurate recommendations. Therefore, address-ing the user cold-start is of great importance from the commercial point of view. Based on the user-group and user-object bipartite networks, we propose a social diffu-sion recommendation algorithm which is able to provide much more accurate recommendations for those small de-gree users than some well-known methods [24]. Finally, we propose a personalized combination of our method and the hybrid method [25], which leads to a further improvement in the overall recommendation performance.
2 Data set and empirical analysis
In the online system we considered, users not only select objects but also join in groups they are in-terested in. Such online system can be represented by two bipartite networks G(U, O, E) and G(U, C, E), where U = {u1, u2, . . . , um}, O = {o1, o2, . . . , on} and C ={c1, c2, . . . , cl} denote the sets of users, ob-jects and communities, respectively. E = {e1, e2, . . . , ep} is the set of links between users and objects and E={e
1, e2, . . . , eq} is the set of links between users and
groups. These two networks can be represented by two adjacency matrixes by Am×nand Bm×l, respectively. The element aiα in Am×n equals to 1 if user i collected α and 0 otherwise, the element bic in Bm×lequals to 1 if user i joined the group c and 0 otherwise.
Two datasets are investigated here: Last.fm1 and Douban2. The Last.fm is a worldwide popular social mu-sic site. As mentioned above, the data we used in this paper consist of two types of data: user-object data and user-group data. The object in the dataset is referred to the artist and the membership refers to the online groups users joined. Douban, launched on March 6, 2005, is a Chinese Web 2.0 web site providing users with rating, re-view and recommendation services for movies, books and music. It is one of the largest online communities in China. Users can view the movies, books and music and also as-sign 5-scale integer ratings (from 1 to 5) to them. In this paper, we only collect users’ activities on the movies and all the groups with movie tag. We treat the user-object in-teraction matrix as binary, that is, the element equals to 1 if the user has viewed or rated the object and 0 otherwise. In both systems, we only sample the users who joined at least one group. The basic statistics of these two datasets are presented in Table 1.
The degree of an object ko is defined as the number of users who collected it and the degree of a group kc is de-fined as the number of users who joined it. For these two datasets, both the object degree and group degree distri-bution follow the power-law form. As shown in Table 1, the group network is much sparser than the user-object network. In this sense, the information extracted from membership identity is relatively limited. However, we will show in next section that this information is cru-cial to improve the accuracy of object recommendation, especially for small degree users.
The degree of a user with respect to the objects is denoted as ku(o) and the degree of a user with respect to the groups is denoted as k(c)u . We present the correlations between k(o)u and k(c)u in the top sub-figures of Figure 1. From the scatter plot, it is clear that there are many users who selected few objects but joined many groups. This is confirmed by the averaged curves (see the red curves). Generally speaking, the correlations between k(o)u and ku(c) in both datasets is weak. Actually, the weak correlation is due to the property of the real systems. Watching a movie or listening to an album is relatively time consuming. Be-fore selecting a movie to watch or an album to listen, a user will check some background information about these objects to make sure they are sufficiently good. In order to get such information, some users may join many relevant groups and read the group mates’ comments. For those users, they may join in many groups but collect only a few objects.
1 http://www.last.fm 2 http://www.douban.com
Fig. 1. The top sub-figures demonstrate the correlation
be-tween the number of a user’s collected objectsk(o)u and joined groups k(c)u . Given a x, the red line is obtained by averaging
ku(c)over all users whoseku(o)equalsx. The bottom sub-figures
show the correlation between users’ similarities based on col-lected objects s(o)ij and joined groupss(c)ij .
We further compare different users’ similarities based on their collected objects and joined groups. Given two users i and j, one can calculate their similarity by com-paring their collected objects as:
s(o)ij = |Γ (o) i Γ(o) j | |Γi(o)Γj(o)|, (1) where Γi(o) and Γj(o) denote the collected object set of i and j, respectively. Besides, we can calculate the similarity between users based on their joined groups,
s(c)ij = |Γ (c) i Γ(c) j | |Γi(c)Γj(c)|, (2) where Γi(c)and Γj(c)denote the joined group set of i and j, respectively. For the sake of clear presentation, we sample 50 users randomly and report the correlation between s(o)ij and s(c)ij in the bottom sub-figures of Figure1. Again, there is no strong correlation.
In next step, we will investigate the potential influence of the social grouping on users’ selection of objects. The analysis is based on the model in reference [13]. In the model, a user u may participate probabilistically in one or more virtual groups (denoted by z) and his/her selection of items is assumed to be linked with these groups. As an example, users in the group z may introduce an object o to user u and u may select or rate it. Therefore, each rating is modeled as a mixture of these virtual groups, which is
Fig. 2. The dependence of p(o, u) on the k(o)
u . For a givenx, its correspondingp(o, u) is obtained by averaging all the users whose k(o)u are in the range of [a(x2− x), a(x2+x)], where a is chosen as 0.5 log 5.
given by
p(o, u) =
z
p(o|z)p(z|u)p(u), (3) where p(u) is the probability to select user u, p(z|u) is the probability to pick a group z from u’s joined groups and p(o|z) is the probability to pick an object o in all the objects selected by users in group z. In reference [13], p(o, u) was claimed to be the potential probability that a user u selects an item o through these virtual groups. Actually, p(o, u) can be also regarded as the probability that a user u finds his/her interested object o from the group mates’ selected objects. If the probability is high, the potential influence of groups on this user’s choice of object is considered to be large. Since the datasets used in this paper consist explicit user-defined groups, the virtual group z can be naturally replaced by the real group c and equation (3) can be rewritten as:
p(o, u) =
c∈C
p(o|c)p(c|u)p(u), (4) where C is the set of groups that user u has joined, p(c|u) is the probability to pick a group c from u’s joined groups and p(o|c) is the probability to pick an object o in all the objects selected by users in group c. Suppose the chance of each group to be selected from a user u’s joined groups set is equal, p(c|u) = 1/ku(c). p(o|c) is the probability that object o is selected by users in group c:
p(o|c) = u∈cauo u∈cau· = u∈cauoα u∈c n α=1auα . (5)
Since u may select more than one object, we obtain p(o, u) by averaging p(o, u) over all his/her collected ob-jects. The dependence ofp(o, u) on k(o)u in both data sets is presented in Figure2.
The negative correlation in Figure2indicates that the small degree users (i.e. users with small k(o)u ) usually have largep(o, u) while those large degree users tend to have
(a) 1 0 0 1 0 1 1 1 0 13/6 4/3 7/6 1/3 2 1/3 13/12 17/12 1/6 (b)
Fig. 3. The illustration of (a) the mass diffusion and (b) the social diffusion processes. The gray square denotes the target user.
Circles represent objects and triangles are the groups.
small p(o, u) in both datasets. That is to say, groups have more potential influence on small degree users when they select objects. Moreover, by comparing p(o, u) of Last.fm and Douban, we find that the former is much larger than the latter. It means that users in Last.fm are much more active in groups and more likely to be influ-enced by groups.
Based on the analysis above, we conclude that the information of social groups can compensate the sparse data in the user-object network. When a user did not choose any object or chose very few objects, we can still use the group information to obtain the similarity be-tween him/her and other users. This is important since it may solve the user cold-start problem in information filtering [24].
3 Information filtering
In recent years, the study of information filtering attracts attention of researchers from different fields including so-cial and computer scientists, physicists, and interdisci-plinary researchers [15]. As we mentioned in the intro-duction, one of the biggest challenges in the information filtering is the user cold-start problem which is very im-portant from the commercial point of view. Solving it not only increases the loyalty of new users, but also stim-ulates the inactive users to use the web site more fre-quently. Previous recommendation algorithms only take into account the user-object network, which makes the in-formation of the new/inactive users very limited [25,26]. Therefore, it is necessary to include also users’ member-ship information [24]. Motivated by the empirical analy-sis above, we propose a social diffusion recommendation algorithm (short for SD algorithm) for improving the rec-ommendation accuracy of small degree users, i.e., solving the user cold-start problem. The basic idea is that one can predict users’ preferences of objects through their mem-bership information though they collected very few objects in the history.
The SD algorithm will be built on the mass diffusion process on both the user-object and user-group bipartite networks. In the original mass diffusion algorithm [26], given a target user i to whom we will recommend objects to, each of i’s collected object is assigned with one unit of
resource and they are equally distributed to all the neigh-boring users who have selected this object. If user j is one of these users, the resource he/she received from o will be 1/ko where ko is degree of o (namely the number of users who collected o). The final resource j received is the sum over all i’s collected objects:
fj(o)=
o∈Γi(o)∩Γj(o)
aio
ko, (6)
where Γi(o) and Γj(o) are i and j’s collected object sets, respectively. We can assign resource to the group mates in the same way in our SD method. Suppose user j has joined a same group c as the target user i, j will receive 1/kc resource from c. The final resource j received is the sum over all i’s joined groups:
fj(c)=
c∈Γ(c)
i ∩Γj(c)
bic
kc, (7)
where Γi(c) and Γj(c) are i and j’s joined group sets, re-spectively. Since i’s neighbors from both group and object point of view are similar users to i, we combine these two kinds of resource as fj = fj(o)+ fj(c). Finally, we let each user distribute their resource fjequally to the neighboring objects. The final resource object o obtained is:
fo=
o ∈ Γj(o)
fj
kj(o), (8)
where kj(o) is the number of objects j collected. The final resources of all objects will be sorted in descending order and the objects with most resources will be recommended. The SD process is illustrated in Figure3b.
Some other well-known recommendation algorithms based on only user-object bipartite network are selected to compare with our method. The first one is the original mass diffusion algorithm [26] (short for MD). It can be expressed by the matrix form−→f= W−→f , where −→f is the initial resource vector on objects and the element wαβ of W is the resource that object α received from object β. The transition matrix W can be computed by:
wαβ= 1 kβ m i=1 aiαaiβ ki . (9)
The final resource vector−→f will be sorted in the descend-ing order and those objects with most resources will be recommended (see Fig.3a for illustration).
The second one is the hybrid method combining the mass diffusion process [26] and the heat conduction pro-cess [25] (short for HDH). Different from the pure mass diffusion algorithm, the transition matrix W in the hybrid method is calculated by:
wαβ = 1 k1−λ α kβλ m i=1 aiαaiβ ki , (10)
where λ is a tunable parameter. If λ = 0, it degenerates to the pure heat conduction algorithm [27]. If λ = 1, it gives the mass diffusion algorithm [26].
Two kinds of collaborative filtering (CF) methods are also considered: the user-based CF (short for UCF ) and the item-based CF (short for ICF ). In UCF, the basic assumption is that similar users usually collect the same items. Accordingly, the recommendation score of object α for target user i is:
piα=
m
j=1
sijajα, (11)
where sij is the similarity between user i and user j. Ac-tually, the measure of similarities between two nodes in a network is subject to the definition [28]. In this paper, we apply the Salton index to measure the similarity between users [29]: sij= n α=1 aiαajα kikj. (12)
Different from the UCF, the basic assumption of ICF is that a user is usually interested in the object similar to the objects already collected by him/her. The recommen-dation scores of α for target user i is:
piα=
n
β=1
sαβaiβ, (13)
where sαβis the similarity between α and β and computed also by the Salton index,
sαβ= m i=1 aiαaiβ kαkβ. (14)
To test the recommendation accuracy of different algo-rithms, the links in the user-object bipartite network are randomly divided into two parts: the training set (ET) and the probe set (EP). The training set contains 80% of the original data and the recommendation algorithm runs on it. The left 20% links forms the probe set which will be used to test the performance of the recommendation results. Note that the node sets (i.e. user sets and items sets) are equal in the training and probe sets.
We use the ranking score metric (RS) to test the accu-racy of algorithms. As discussed above, each recommen-dation algorithm can provide each user an ordered list of
Fig. 4. Dependence of mean cumulative ranking score RS on
the user degreeku(o). Given a user degreek(o)u ,RS is obtained by averaging the ranking score over all the users whose degrees are no larger thanku(o). The optimalλ of HDH is 0.3 for Douban and 0.4 for Last.fm, respectively. The insets are the dependence of overall RS on the parameter β in SD + HDH. The error bars are the standard deviation ofRS in different division of probe sets and training sets. In the bottom sub-figures,β is set as the optimal value according to the results in the insets.
his/her uncollected objects. For a user i, if the object α is in the probe set, we measure the position of this object α in the order list. For example, if there are 1000 uncollected objects for i and α is the 30th from the top in the order list, we say the position of α is the top 30/1000, and the ranking score Riα = 0.03. A good algorithm is expected to give a small ranking score.
The top sub-figures of Figure 4 give the relationship between the user degree ku(o) and the mean cumulative ranking score RS. Given a user degree ku(o), the mean cumulative ranking score RS is obtained by averaging over all the users whose degrees are no larger than k(o)u . In Figure 4, it shows that the hybrid method gives the best mean ranking score over all users (see theRS when user degree is maximum). Compared to the MD method, the SD method works better in overall ranking score. Among all these methods, the UCF gives the worst overall ranking score.
In recommender systems, it is usually difficult to rec-ommend objects to the users who have collected a few objects. For the small degree users, the accuracy of the hybrid method (HDH) is not so good as the other meth-ods in both datasets. The UCF is better than the ICF when recommending objects to those small-degree users. The performance of the MD method is similar to the UCF
method. Among all methods considered, the SD method achieves the lowest ranking score when recommending ob-jects for small-degree users, which indicates that the SD method is very effective in solving the user cold-start prob-lem. Actually, considering the social grouping in recom-mendation will bring much value information for the small degree users. Compared to small degree users, large degree users have less common tastes with their group mates. As shown in Figure 2, p(o, u) keeps decreasing with k(o)u . Therefore, the information of groups should be considered less when recommending objects for large degree users.
Based on the results above, we conclude that the use of recommendation algorithms should be personalized. In other words, it is better to apply different recommenda-tion algorithms for different users. For instance, we can use the social diffuse method to generate recommendations for the small degree users and use the hybrid method for large degree users. In this way, we can effectively improve the recommendation accuracy for the small degree users. At the same time, the recommendation accuracy for the large degree users can be well preserved. Here, we propose a per-sonalized combination of SD and HDH methods. Denote hiαand giαas the resource item α received from user i by HDH and SD methods, respectively. The final recommen-dation score of item α to user i can be expressed as:
fiα= λihiα+ (1− λi)giα, where λi = ( k(o)i
max(k(o))β and k(o)i is the degree of user i.
When β = 0, all the users are using HDH. When β is in-finitely large, all the users are using SD. As β increases, the recommendation method changes smoothly from HDH to SD, and the small degree users change faster than large gree users. As such, SD will have more weight in small de-gree users’ recommendation. This combination is denoted as SD + HDH. The result is presented in the bottom sub-figures of Figure4. From the insets, one can see that the overall RS is improved by adjusting β and there is an optimal β. The small error bars indicate that the optimal β is stable in different divisions of probe set and training set. Therefore, in practical use, the future optimal β can be estimated by testing the historical data. For the small degree users, the recommendation accuracy can be sig-nificantly improved by the SD + HDH method. We recall that users in the Last.fm are more active in communities. Therefore, the new method achieves a better accuracy im-provement in Last.fm than in Douban dataset.
4 Conclusion
In summary, we investigate the online system coupled with user-object and user-group bipartite networks. Our results show that users may join in many groups though they have collected a few objects. Based on the Aspect Model [13], we find that the group mates of the small degree users share very similar tastes with them (i.e., their selected objects are similar). We further propose a recommenda-tion method which takes into account the informarecommenda-tion
of users’ membership (i.e. the group that users joined). Our method can largely improve recommendation accu-racy for the small degree users. However, this social diffu-sion method does not work well for the large degree users. By combining the new method and the hybrid method in reference [25], we achieve a higher recommendation ac-curacy than the original hybrid method itself, especially on the small-degree users. The user cold-start problem is effectively solved by our method. Finally, we remark that this work highlights that different users should be assigned with their own suitable recommendation methods, which may lead to a significant improvement of the recommen-dation performance in the future.
This work is supported by the opening foundation of Insti-tute of Information Economy in Hangzhou Normal University (Grant No. PD12001003002002), the Sichuan Provincial Sci-ence and Technology Department (Grant No. 2012FZ0120) and NSFC (61370150). W.Z. acknowledges the support from Sino-Swiss Science and Technology Cooperation Program (EG57-092011) and the Program of Outstanding PhD Candidate in Academic Research by UESTC (YBXSZC20131029). A.Z. ac-knowledges the support from China scholarship Council.
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![Fig. 2. The dependence of p(o, u) on the k u (o) . For a given x, its corresponding p(o, u) is obtained by averaging all the users whose k (o)u are in the range of [ a ( x 2 − x ) , a ( x 2 + x )], where a is chosen as 0](https://thumb-eu.123doks.com/thumbv2/123doknet/14871275.639981/3.892.70.435.142.473/dependence-given-corresponding-obtained-averaging-users-range-chosen.webp)
